A331857 a(n) is the greatest value obtained by partitioning the binary representation of n into consecutive blocks, and then reversing those blocks.

0, 1, 2, 3, 4, 6, 6, 7, 8, 12, 12, 14, 12, 14, 14, 15, 16, 24, 24, 28, 24, 26, 28, 30, 24, 28, 28, 30, 28, 30, 30, 31, 32, 48, 48, 56, 48, 52, 56, 60, 48, 52, 52, 58, 56, 58, 60, 62, 48, 56, 56, 60, 56, 58, 60, 62, 56, 60, 60, 62, 60, 62, 62, 63, 64, 96, 96

Offset: 0

Author

Rémy Sigrist, Jan 29 2020

Keywords

• nonn
• base

Examples

			For n = 6:
- the binary representation of 6 is "110",
- we can split it in 4 ways:
      "110" -> "011" -> 3
      "1" and "10" -> "1" and "01" -> 5
      "11" and "0" -> "11" and "0" -> 6
      "1" and "1" and "0" -> "1" and "1" and "0" -> 6
- we have 3 distinct values, the greatest being 6,
- hence a(6) = 6.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..16384
• Rémy Sigrist, PARI program for A331857
• Index entries for sequences related to binary expansion of n

Crossrefs

See A331855 for the number of distinct values, and A331856 for the least value.

Cf. A023416, A023758, A073138.

Programs

PARI

See Links section.

Formula

a(n)^A023416(n) = A073138(n) (where a^k denotes the k-th iterate of n).

a(n) >= n with equality iff n belongs to A023758.